A style of dressing up, where the person wears a powder wig (like guys wore during colonial times), a scholarly robe, and a cape. It looks ridiculous, and it draws attention to the person dressed like this, but the person in this type of outfit is usually mentally unstable and thinks that dressing like this is a manifestation of their "glory".

What type of event is this dinner supposed to be? What's the dress code?

There's a lot of variation in how people will be dressed. Dennis is attending in business casual, Meredith is going in semi-formal, and Mel is going in full glory.